The long term objective of this research is to understand the possible neural mechanisms underlying the learning of simple cognitive procedures such as arithmetic through neural network modeling of the process. The specific goals are: (1) To implement and test a neural network model of addition. (2) To analyze how the network has solved the task and evaluate it with respect to the human data. (3) To lesion the network and analyze its behavior with reference to human data. (4) To determine the optimal method of retraining the network after damage. Neural network of addition have been done before, but only for single digit addition. The difference here is the attempt to model the sequential process of addition in a parallel network. The network will be trained in this task via the back propagation algorithm. We will use recurrent networks that record their processing history in their state so that the network can use this information to keep track of where it is in the procedure. Once the network has learned the task, standard techniques will be applied to analyze how the network has solved the task. Also at this stage, random lesions may be introduced into the network, which allow comparison of its behavior with that observed in humans. Finally, the network will then be retrained on the task to determine the optimal method of retraining. This will have obvious implications for the treatment of brain damaged patients with acalculia. Thus exploring the behavior of networks trained to do these tasks, we hope to learn better ways of training children and retraining lesion patients.